Neuromorphic computing aims to emulate biological neural functions to overcome the memory bottleneck challenges with the current Von Neumann computing paradigm by enabling efficient and low-power computations. In recent years, there has been a tremendous engineering effort to bring neuromorphic computing for processing at the edge. Oscillatory Neural Networks (ONNs) are brain-inspired neural networks made of oscillators to mimic neuronal brain waves, typically visible on Electroencephalograms (EEG). ONNs provide massive parallelism using coupled oscillators and low power computation using oscillator phase dynamics. In this paper, we present for the first time how to use ONNs to perform obstacle avoidance on a mobile robot. Digitally implemented ONNs on FPGA are used and configured for obstacle avoidance inside the industrial surveillance robot E4 from the company, A.I.Mergence. We show that ONNs can perform real-time obstacle avoidance based on the sensory data from proximity sensors embedded on the E4 robot. The highly parallel architecture of ONNs not only allows fast real-time computation for obstacle avoidance applications but also opens up a novel computing paradigm for edge AI to enable low power and real-time sensing to action computing.